A synthetic fiber used in manufacturing carpet has tensile strength (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample mean tensile strength that exceeds 10.5 psi. (a) Recall the exact distribution on P. 16 of Chapter 7 note, we have x (na, nλ). What is the probability that the sample mean exceeds 10.5 psi? (b) Using the central n limit theorem, we have x ~AN(, α -). What is the λ 2 λη probability that the sample mean - exceeds 10.5 psi? (c) Are the results in (a) and (b) similar? Which one is more "reliable" when = 10 ? (d) Repeat (a) and (b) with n = 1J0 ar the esults similar? (c) Are the results in (a) and (b) similar? Which one is more "reliable" when n=10? (d) Repeat (a) and (b) with n = 1000, are the results similar?
A synthetic fiber used in manufacturing carpet has tensile strength (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample mean tensile strength that exceeds 10.5 psi. (a) Recall the exact distribution on P. 16 of Chapter 7 note, we have x (na, nλ). What is the probability that the sample mean exceeds 10.5 psi? (b) Using the central n limit theorem, we have x ~AN(, α -). What is the λ 2 λη probability that the sample mean - exceeds 10.5 psi? (c) Are the results in (a) and (b) similar? Which one is more "reliable" when = 10 ? (d) Repeat (a) and (b) with n = 1J0 ar the esults similar? (c) Are the results in (a) and (b) similar? Which one is more "reliable" when n=10? (d) Repeat (a) and (b) with n = 1000, are the results similar?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 7E
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Transcribed Image Text:A synthetic fiber used in manufacturing carpet has
tensile strength (in psi) following gamma distribution
with a 1 and λ = 0.1. Find the probability that a
random sample of n = 10 fiber specimens will have
sample mean tensile strength that exceeds 10.5 psi. (a)
Recall the exact distribution on P. 16 of Chapter 7 note,
we have x ~(na,nλ). What is the probability that the
n
sample mean exceeds 10.5 psi? (b) Using the central
α
limit theorem, we have x -AN( ~, x). What is the
2
λ
λη
probability that the sample mean - exceeds 10.5 psi? (c)
Are the results in (a) and (b) similar? Which one is more
"reliable" when = 10 ? (d) Repeat (a) and (b) with
10?
n 1 JO ar the esults similar?
(c) Are the results in (a) and (b) similar? Which one is more "reliable"
when n=10?
(d) Repeat (a) and (b) with n = 1000, are the results similar?
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